ashrae 2014 evaporation paper.pdf

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2014 ASHRAE. THIS PREPRINT MAY NOT BE DISTRIBUTED IN PAPER OR DIGITAL FORM IN WHOLE OR IN PART. IT IS FOR DISCUSSION PURPOSES ONLYAT THE 2014 ASHRAE ANNUAL CONFERENCE. The archival version of this paper along with comments and author responses will be published in ASHRAETransactions, Volume 120, Part 2. ASHRAE must receive written questions or comments regarding this paper by July 21, 2014for them to be included in Transactions.

ABSTRACT

The calculation of evaporation is required from a variey

of water pools including swimming pools, water storage tanks

and vessels, spent fuel pools in nuclear power plants, etc. The

author has previously published formulas for the calculation

of evaporation from occupied and unoccupied indoor swim-

ming pools, which were shown to agree with all available test

data.In thispaper, evaporationfrom manytypes of water pools

and vessels is discussed and formulas are provided for calcu-

lating evaporation from them. These include indoor and

outdoor swimming pools (occupied and unoccupied), spent

nuclear fuel pools, decorative pools, water tanks, and spills.

Look-up tables are provided for simplifying manual calcula-

tions.

INTRODUCTIONThis paper attempts to provide reliable methods for the

calculation of evaporation from many types of water pools,

tanks, vessels, and spills. The author has previously published

formulas for the calculation of evaporation from occupied and

unoccupied indoor swimming pools, which were validated

with allavailabletest data (Shah1992, 2008, 2012a,2013) and

are widely used. The calculation of evaporation is also

required for many other applications and situations. In this

paper, in addition to the authors published correlations for

indoor swimming pools, formulas and methods are also

provided for the calculation of evaporation for the following:

Outdoor occupied and unoccupied swimming pools

Pools with hot water, such as spent nuclear fuel pools

Decorative pools

Pools used for heat rejection from refrigeration systems

Vessels/tanks with low water level

Water spills

The calculation methods presented are based on physicalphenomena, theory, and test data.

MECHANISM OF EVAPORATION

Consider evaporation from an undisturbed water surface,

such as that of an unoccupied swimming pool. A very thin

layer of air, which is in contact with water, quickly gets satu-

rated due to molecular movement at the air-water interface. If

there is no air movement at all, further evaporation proceeds

entirely by molecular diffusion, which is a very slow process.

On the other hand, if there is air movement, this thin layer of

saturated air is carried away and is replaced by the compara-

tively dry room air and evaporation proceeds rapidly.

Thus, it is clear that for any significant amount of evapo-

ration to occur, air movement is essential. Air movement can

occur due to two mechanisms:

1. Air currents caused by the building ventilation system for

indoor pools and wind for outdoor pools. This is the

forced convection mechanism.

2. Air currents caused by natural convection (buoyancy

effect). Room air in contact with the water surface gets

saturated and thus becomes lighter compared to the room

air, and therefore moves upwards. The heavier and drier

room air moves downwards to replace it.

For outdoor swimming pools, forced convection is

usually the prevalent mechanism. For indoor pools, natural

convection mechanism usually prevails while most published

formulas have considered only forced convection.

Methods for Calculation of Evaporation fromSwimming Pools and Other Water Surfaces

Mirza Mohammed Shah, PE, PhDFellow/Life Member ASHRAE

Mirza Mohammed Shahis an independent consultant, Redding, CT.

SE-14-001


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2 SE-14-001

UNOCCUPIED INDOOR SWIMMING POOLS

Present Authors Method

Shah developed formulas for evaporation from undis-

turbed water surfaces, which starting with Shah (1981), went

through several modifications (Shah 1990, 1992, 2002, 2008).The final version is in Shah (2012), according to which the

evaporation rateE0 is thelarger of those given by thefollowing

two equations:

(1)

(2)

withC= 35 in SI units andC= 290 in I-P units,b= 0.00005

in SI andb= 0.0346 in I-P units.

Equation 1 is the evaporation due to natural convectioneffect. It was derived using the analogy between heat and mass

transfer. The derivation is given in the Appendix. Equation 2

shows the evaporation caused by the air currents produced by

the building ventilation system. This was obtained by analyzing

the test data for negative density difference as shown in Figure

1. The reasoning was that as natural convection essentially

ceases under such conditions, allthe evaporationmust be occur-

ring due to forced convection. As noted by theASHRAE Hand-

bookHVAC Applications (ASHRAE 2007), air velocities in

typical swimming pools range between 0.05 and 0.15 m/s(10 to

30 fpm). The computational fluid dynamics (CFD) simulations

by Li and Heisenberg (2005) of a large swimming pool showed

very complex airflow patterns along the surface and height of

the pool, but the velocities within 1 m (3 feet) of the water

surface were also in this range. Equation 2 is therefore consid-

ered applicable to velocities up to 0.15 m/s (30 fpm).

This method was validated by comparison with test data

from 11 sources in Shah (2012b). Table 1 gives the range of

parameters in each of these data sets. In Shah (2008), the same

database (except the data of Hyldegard [1990]) was also

compared to the ten published correlations listed in Table 2.

Table 3 gives the results of these data analyses. It is seen that

the 113 data points were predicted by the Shah formulas with

a mean absolute deviation of 14.5% giving equal weight to

each data set. All the other correlations gave much inferior

agreement with datal; thus, the Shah method is the most reli-

able among available methods and therefore may be used for

practical calculations.

For ease of calculation using the Shah method, Equations

1 and 2 and Tables 4 and 5 have been prepared. These tables

give the evaporationratesat discrete values of temperature and

humidity in the range that may occur in swimming pools.

Evaporation at intermediate values can be obtained by linear

interpolation.

Various Formulas for Undisturbed Water Pools

Many researchers performed tests in which air was blown

or drawn over water surfaces and correlated their own test data

in the form:

(3)

Where a andb are constants andu is the air velocity.

Table 2 lists several such correlations. These are applied toindoor pools by inserting u 0. Such formulas do not takeintoaccount natural convection, which depends on air density

difference, and hence cannot be expected to be generally

applicable to indoor pools in which natural convection effects

are prevalent. This was pointed out by early researchers. For

example, Himus and Hinchley (1924) performed tests on

evaporation by natural convection as well as with forced

airflow and gave formulas for both cases. They found that

their forced convection formula extrapolated to zero velocity

predicts three times their formula for natural convection.

Lurie and Michailoff (1936) stated that forced convection

equations should not be extrapolated to zero velocity as they

will give erroneous results. Nevertheless, such formulas have

continued to be proposed. The best known among such

formulas is that of Carrier (1918) which is recommended by

ASHRAE (2011) with correction factors called activity

factors.

Many other researchers performed tests under natural

convection conditions and correlated their own data by formu-

las of the form:

(4)

E0 Cw r w 1/ 3

Ww Wr =

E0 b pw pr =

Figure 1 Analysis of data at negative density difference to

obtain Equation 2 for forced convection evapo-ration in indoor pools. 1 Pa= 2.953E-4 in. Hg, 1

kg/m2h = 0.205 lb/ft2h.

E a bu+ pw pr =

E a pw pr n

=


3/15

SE-14-001 3

Wherea andn are constants. Such formulas do not take into

account density difference, which determines the intensity of

natural convection, and hence cannot be expected to be gener-

ally applicable.

Many of the correlations of the type of Equations 3 and 4

are listed in Table 2. As is seen in Table 3, these give poor

agreement with most data.

OCCUPIED INDOOR POOLS

Experience shows that evaporation from occupied pools

is higher than from unoccupied pools. This increase is attrib-

uted to an increased area of contact between air and water due

to waves, sprays, wet bodies of occupants, and wetting of

deck. As deck area is usually comparable to the pool area,

wetted deck represents the largest increase in air-water contact

area. Theair-water contact area is expectedto increase with an

increasing number of occupants. A number of formulas have

been published according to which the increase in evaporation

compared to unoccupied pools depends only on the number of

occupants (Hens 2009; Smith et al. 1999; Shah 2003). The

basic assumption in these formulas is that the rate of evapora-

tion from the increased air-water contact area is the same as

from the pool area.

Shah (2013) pointed out that the rate of evaporation fromthe wetted deck area may not be the same as from the pool

surface. Water spilled on the deck will quickly cool down,

approaching the wet-bulb temperature. If the pool water

temperature is higherthan theair temperature,the rate of evap-

oration from the wetted deck will be much lowerthan from the

pool surface as the density difference between air and water

will be much lower at the deck, reducing the natural convec-

tion intensity. On the other hand, if the water and air temper-

atures are about equal, the rate of evaporation from the wetted

deck will be comparable to that from the pool surface. Thus,

Table 1. Range ofTest Data for Undisturbed Water Pools

with which Equations 1 and 2 and Other Formulas were Compared

ResearcherPool Area

Water

Temp. Air Temp.

RH,

%

pwprEvaporation

Rate,Notes

m2 ft2 C F C F Pa in. Hg kg/m3 lb/ft3 kg/m2h lb/hft2

Hyldegard

(1990) 418 4493 26.1 79.0 28.5 83.3 37 1944 0.574 0.0134 8.4E-4 0.125 0.026 1

Bohlen

(1972) 32 344 25.0 77.0 27.0 80.6 60 1029 0.303 0.0043 2.7E-4 0.052 0.011 1

Boelter et al.

(1946) 0.073 0.78

24.0

94.2

75.2

201.6

18.7

24.7

65.7

76.5

64

98

1272

80156

0.375

23.7

0.022

1.0025

1.4E-3

0.062

0.082

21.07

0.016

4.2 2

Rohwer

(1931) 0.837 9.0

7.1

16.5

44.5

61.7

6.1

17.2

43.0

63.0

69

78

247

638

0.073

0.188

0.0049

0.0080

3.1E-4

5.0E-4

0.010

0.040

0.0021

0.0082 2

Sharpley and

Boelter (1938) 0.073 0.78

13.9

33.4

57.0

92.1 21.7 71.1 53

210

3786

0.062

1.12

0.0049

0.088

-3.1E-4

5.5E-3

0.018

0.402

0.0036

0.0804 2

Biasin &Krumme

(1974)

62.2 668 24.3

30.1

75.7

86.2

24.3

34.6

75.7

94.3

40

68

1010

2128

0.298

0.628

0.0007

0.030

4.4E-5

1.9E-3

0.030

0.154

0.006

0.0301 1

Sprenger (c.

1968) 200 2150 28.5 83.3 31.0 87.8

54

55

1422

1467

0.420

0.433

0.0070

0.0076

4.4E-4

4.7E-4

0.070

0.235

0.014

0.047 1

Tang et al.

(1993) 1.13 12.1 25.0 77.0 20.0 68.0 50 2001 0.591 0.0433 2.7E-3 0.168 0.034 2

Reeker

(1978) Note 3 23.0 73.4 25.5 77.9 71 493 0.145 0.004 2.5E-4 0.0265 0.054. 1, 3

Smith et al.

(1993) 404 4343 28.3 82.9

21.7

27.8

71.1

82.0

51

73

1127

1990

0.332

0.588

0.0150

0.0554

9.4E-4

3.5E-3

0.090

0.246

0.018

0.049 1

Doering

(1979) 425 4568 25.0 77.0 27.5 81.5 28 2142 0.632 0.0153 9.4E-4 0.175 0.035 1

All Sources 0.073

425.0

0.78

4568

7.1

94.2

44.5

201.6

6.1

34.6

43.0

94.3

28

98

210

80156

0.062

23.7

0.004

+1.002

2.5E-4

+0.065

0.010

21.073

0.002

4.202

Notes: 1. Field tests on swimming pool 2. Laboratory tests 3. Private pool, size not given

r w


4/15

4 SE-14-001

the increase in evaporation due to occupancydepends not only

on the number of occupants but also the density difference

between room air and the air in contact with the pool surface.

Accordingly, Shah presented the following formula for evap-

oration from occupied pools:

ForN*0.05,

(5)

whereN* is the number of occupants per unit pool area. For

N* < 0.05, perform linear interpolation between Eocc/E0 at

N* = 0.05 persons/m2 (0.0046 persons/ft2) andEocc/E0= 1 at

N* = 0. For (rw) < 0, use (rw) = 0.E0is calculatedby the Shah (2012) method, larger of Equations 1 and 2.

In Figure 2, predictions of Equation 5 are plotted together

with the predictions of the correlations of Hens (2009) and

Smith et al. It is seen that at= 0.05 kg/m3 (0.0031 lb/ft3),the predictions of Equation 5 and those of Smith et al. (1999)

are almost identical. For= 0, the predictions of Equation 5are fairly close to the Hens formula. The formulas of Smith et

al. and Hens were based entirely on their own data. The differ-

ence in their predictions is because of the different air and

water conditions in their respective tests. Smith et al. (1993)

report that water temperature was 28.3C (83F) and the air

temperature varied from 21.6C to 27.8C (71F to 82.0F),

with relative humidity from 51% to 73%; these conditions

indicate that was high. In the tests reported by Hens, air

temperature was higher than water temperature; these condi-

tions indicate thatwas small during the tests.

Equation 5 was compared to test data from four sources

(all that could be found); the range of those data is listed inTable 6. The data were predicted with a mean absolute devia-

tion of 18%, with deviations of 87% of the data within 30%.The same data were also compared with Shah (2003) phenom-

enological and empirical correlations,ASHRAE Handbook

HVAC Applicationsmethod (2007), and the formulas of Hens

(2009), Smith et al. (1993), and VDI (1994). These correla-

tions are listed in Table 7. The results of the comparison are in

Table 8. While the Shah (2003) correlations performed fairly

well, the others gave poor agreement. Thus Shah (2013),

Equation 5, is easily the most reliable correlation for occupied

pools.

For ease in hand calculations with Equation 5, Tables 9

and 10 list the density differences in the range of air and water

conditions typical for indoor swimming pools. Hand calcula-

tions canbe done easilyusingTable 9 or 10 together with Table

4 or 5, depending on the units being used.

Table 11 lists comparison of some individual data points

for occupied and unoccupied indoor swimming pools with

various formulas. It is seen that the Shah (2013) formula gives

much better agreement with the data.

Table 2. Various Empirical Correlations for Undisturbed Water Pools

Author Correlation, SI Units Correlation, IP Units Note

Carrier (1918)

Smith et al. (1993)

Biasin and Krumme

(1974)

Rohwer (1931)

Boelter et al. (1946)

Forx


5/15

SE-14-001 5

Table 3. Results of Comparison of Data for Undisturbed Water Pools from All Sources with All Formulas

Data of

Number

of Data

Points

Percent Deviation From Correlation of Mean Absolute Average

Biasin

and

Krumme

Box Leven Rohwer

Himus

and

Hinchley

Boelter

et al.,

Formula 2

Boelter

et al.,

Formula 1

Tang

et al. Carrier

Smith

et al. Shah Notes

Rohwer

(1931) 40

310.3

310.3

74.6

69.8

40.6

19.9

21.2

6.2

86.2

81.9

44.4

28.4

35.0

5.3

52.3

42.4

210.5

210.4

137.4

135.9

34.2

12.0

Bohlen

(1972) 1

57.1

57.1

54.0

54.1

49.9

49.9 NA

104.5

104.5

47.4

47.4

16.7

16.7

60.5

60.5

181.5

181.5

111.1

111.1

1.0

1.0

Smith et al.

(1993) 5

56.5

56.5

20.1

20.1

9.0

9.0

30.8

5.4

17.7

17.7

14.3

14.3

27.6

27.6

10.1

10.1

45.3

45.3

9.5

9.5

18.7

18.7

Boelter

et al. (1946) 24

49.6

49.6

44.6

4.3

27.7

27.7

188.9

188.9

31.9

31.4

7.5

0.1

7.3

3.0

9.9

4.3

28.2

8.0

30.6

17.9

12.0

10.2

Sharpley

and Boelter

(1938)

29 59.2

59.2

39.8

21.1

35.1

31.0

65.9

55.6

72.7

71.9

31.3

24.8

10.1

0.9

38.6

35.3

121.4

121.4

68.4

68.2

16.9

9.0

Biasin and

Krumme

(1974)

1 18.7

18.7

63.0

63.0

76.5

76.5 NA

132.4

132.4

68.7

68.7

34.8

34.8

82.1

82.1

198.0

198.0

126.5

126.5

6.1

6.1 1

9 16.0

1.0

63.0

63.0

89.7

89.7

40.2

19.6

143.8

143.8

77.9

77.9

67.8

67.8

91.0

91.0

198.0

198.0

126.5

126.5

31.5

31.5 2

Tang et al.

(1993) 1

41.0

41.0

7.3

7.3

10.1

10.1

58.6

58.6

40.5

40.5

2.7

2.7

0.0

0.0

9.8

9.8

69.4

69.4

28.7

28.7

7.7

7.7

Reeker

(1978) 1

156.9

156.9

8.6

8.6

15.3

15.3 NA

24.4

24.4

11.6

11.6

39.4

39.4

1.2

1.2

98.6

98.5

48.8

48.8

7.0

7.0

Doering

(1979) 1

37.0

37.0

4.8

4.8

15.5

15.5 NA

40.5

40.5

2.7

2.7

9.9

9.9

9.8

9.8

69.4

69.4

27.0

27.0

21.9

21.9

Hyldegard(1990)

1 Note 3 Note 3 Note 3 Note 3 Note 3 Note 3 Note 3 Note 3 Note 3 Note 3 5.05.0

All Data

113 137.2

135.9

52.5

32.8

39.2

30.4

74.4

60.6

73.2

71.4

34.1

24.3

25.8

3.9

40.7

32.8

136.2

132.1

86.8

76.4

22.73

10.2 4

82.7

82.7

40.6

33.3

39.3

26.5

67.6

67.6

76.6

76.6

34.5

29.3

24.9

2.2

36.5

33.5

121.8

121.8

71.3

67.7

14.5

2.0 5

Note: 1. Pool area 200 m2. 2. Pool area 62.2 m2. 3. Not evaluated. 4. Giving equal weight to each data point. 5. Giving equal weight to each data set.

a e . vaporat on rom noccup e n oor w mm ng oo s y t e a ormu as n n ts

Water

Temp.,

C

Evaporation from Unoccupied Pool (E0), Space Air Temperature, and Relative Humidity

25C 26C 27C 28C 29C 30C

50% 60% 50% 60% 50% 60% 50% 60% 50% 60% 50% 60%

25 0.1085 0.0809 0.0917 0.0636 0.0732 0.0515 0.0639 0.0450 0.0583 0.0382 0.0523 0.0311

26 0.1333 0.1042 0.1171 0.0872 0.0997 0.0693 0.0806 0.0547 0.0679 0.0479 0.0620 0.0408

27 0.1597 0.1289 0.1433 0.1118 0.1262 0.0941 0.1081 0.0753 0.0885 0.0582 0.0723 0.0510

28 0.1877 0.1556 0.1711 0.1380 0.1539 0.1200 0.1360 0.1014 0.1171 0.0818 0.0968 0.0618

29 0.2174 0.1841 0.2006 0.1661 0.1831 0.1477 0.1651 0.1287 0.1463 0.1092 0.1268 0.0888

30 0.2491 0.2146 0.2319 0.1962 0.2142 0.1773 0.1959 0.1579 0.1771 0.1380 0.1575 0.1176


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6 SE-14-001

Pool Occupancy Limits

According to the International Building Code 2006, the

maximum allowable occupancy in swimming pools is 4.6 m2

(50 ft2) of pool surface area per person. This code has been

adapted in many parts of the world. In the U.S., each state and

almost every town has its own code. Some of them have incor-

porated the International Building Code while some have not

done so. Local authorities should be contacted to find the

applicable regulations.

Recommended Calculation Procedure

The following calculation procedure is recommended:

For unoccupied swimming pools, calculate evaporation

with Equations 1 and 2 and use the larger of the two.

For occupied swimming pools, calculate E0 as above

and then apply Equation 5.

OUTDOOR SWIMMING POOLS

Unoccupied Pools

Natural convection effects in outdoor pools will be thesame as in indoor pools. The difference will be in the

forced-convection effects. In indoor pools, airflow is due to

building ventilation system, while airflow on outdoor pools

is due to wind. If there were no obstructions such as trees

and buildings, evaporation could be calculated using the

analogy between heat and mass transfer considering the

pool surface to be a heated plate. With this approach, Shah

(1981) derived a simplified equation for evaporation due to

wind velocity, which is given in the Appendix. That equa-

tion is applicable if there are no obstructions around the

pool. This is also the case for equations developed from

wind tunnel tests. Most outdoor pools are located close to

buildings and trees which distort the airflow streams.

Hence, formulas developed from tests on actual swimming

pools are preferable. The only one found in the literature is

that by Smith et al. (1999) who measured evaporation from

an unoccupied outdoor swimming pool and fitted the

following equation to their test data:

(6)

Table 5. Calculated Evaporation Rate from Unoccupied Pools at

Typical Design Conditions by the Shah (2012a) Method in I-P Units

Water

Temp.,

F

Evaporation from Unoccupied Pool (E0) Space Air Temperature and Relative Humidity

76F 78F 80F 82F 84F 86F

50% 60% 50% 60% 50% 60% 50% 60% 50% 60% 50% 60%

76 0.0213 0.0159 0.0176 0.0120 0.0135 0.0099 0.0123 0.0085 0.0110 0.0069 0.0097 0.0053

78 0.0269 0.0211 0.0232 0.0173 0.0193 0.0133 0.0149 0.0106 0.0132 0.0091 0.0118 0.0075

80 0.0327 0.0266 0.0291 0.0228 0.0252 0.0188 0.0212 0.0146 0.0166 0.0114 0.0141 0.0097

82 0.0390 0.0326 0.0353 0.0287 0.0314 0.0246 0.0274 0.0204 0.0232 0.0160 0.0185 0.0122

84 0.0458 0.0391 0.0420 0.0350 0.0381 0.0309 0.0340 0.0266 0.0298 0.0222 0.0253 0.0176

86 0.0530 0.0461 0.0492 0.0419 0.0452 0.0377 0.0410 0.0333 0.0368 0.0288 0.0323 0.0241

88 0.0608 0.0536 0.0569 0.0494 0.0528 0.0450 0.0486 0.0405 0.0442 0.0358 0.0397 0.0311

90 0.0692 0.0618 0.0651 0.0574 0.0610 0.0529 0.0567 0.0482 0.0522 0.0435 0.0476 0.0386

Figure 2 Comparison of the Shah formula (2013) Equation

5 with the correlations of Hens (2009) and Smith

et al. (1999) at two values of air density differ-

ence, in lb/ft3, 1 lb/ft3 = 16kg/m3, 1 ft2 = 0.093 m3.

E0 C1 C2u+ pw pa /ifg=


7/15

SE-14-001 7

Table 6. Range of Data for which the Shah (2013) Formula for Occupied Indoor Pools has Been Verified

Source Pool Area,

m2 (ft2)

Persons,

per m2 (per ft2)

Air Temp.,

C (F)

RH,

%

Water Temp.,

C (F)

,

kg/m3 (lb/ft3)

(pwpr),

Pa (in. Hg)

Doering (1979) 425

(4575)

0.082 (0.008)

0.167 (0.017)

27.5 (81.5)

29.0 (84.2)

33

41 25.0 (77)

0.0024 (0.00015)

0.0153 (0.00096)

1526 (0.45)

2141 (0.63)

Biasin and

Krumme (1974)

64

(689)

0.016 (0.0015)

0.325 (0.03)

26.0 (78.8)

30.0 (86.0)

46

72

26.0 (78.8)

30.0 (86.0)

0.0013 (8 105)

0.0313 (0.0019)

1067 (0.31)

2087(0.62)

Heimann andRink

(1970)

200

(2153)

0.10 (0.0093)

0.325 (0.039) 31.0 (87.8)

54

55 28.5 (83.3) 0.007 (0.00044) 1422 (0.42)

Hanssen and

Mathisen (1990)

72

(774)

0.028 (0.037)

0.486 (0.045) 30.0 (86.0)

60

65 32.0 (89.6)

0.0312 (0.00195)

0.0421 (0.0026)

2084 (0.62)

2377 (0.70)

All Data 64(689)

425(4575)

0.016 (0.0015)

0.486 (0.045)

26 (78.8)

31 (87.8)

32

72

25 (77)

32 (89.6)

0.0013 (8 105)

0.0421 (0.0026)

1067 (0.37)

2377 (0.7)

r w

Table 7. Various Correlations for Occupied Pools which Were Evaluated Together with Equation 5

Correlation of SI Units I-P Units

ASHRAEHandbook

HVAC Applications

(2007)

Smith et al. (1999)

VDI (1994)

Hens (2009)

Shah (2003)

Empirical

Shah (2003)

Phenomenological

E/E0 =3.3FU+ 1 for FU< 0.1

E/E0 =1.3FU+1.2 for0.1 FU1E/E0 = 2.5 for FU> 1

E/E0 =3.3FU+1 for FU< 0.1

E/E0= 1.3FU+ 1.2 for 0.1FU1E/E0 = 2.5 for FU> 1

E 0.000144 pw pr = E 0.1 pw pr =

E 0.0000106 1.04 4.3N*+ pw pr = E 0.0072 1.04 46.3N*+ pw pr =

0.0000204 1 8.46N*+ = pw pr E 0.014 pw pr =

0.0000409 1 8.46N*+ pw pr = E 0.028 1 91N*+ = pw pr

E 0.113 0.000079/FU 0.000059+ pw pr = 0.0226 0.000016/FU 0.04+ pw pr =

Table 8. Deviations of Various Formulas for Occupied Pools withTest Data

Data of

Evaluated Formulas

ASHRAE

(2007)

VDI

(1994)

Smith

et al. (1999)

Hens

(2009)

Shah (2003)

Empirical

Shah (2003)

Phenom.

Shah (2013)

Equation 5

Doering (1979)15.3 60.2 20.6 42.8 -0.4 24.3 7.0

17.2 60.2 21.5 42.8 6.0 29.1 23.9

Hanssen andMathisen (1990)34.2 -8.6 28.6 51.0 49.0 27.0 18.7

34.2 26.4 28.6 51.0 49.0 27.0 20.1

Heimann and Rink (1970)4.5 32.7 16.6 25.4 8.1 26.1 5.5

13.0 32.7 16.6 25.4 14.3 26.1 8.1

Biasin and Krumme (1974)39.9 94.3 36.2 38.8 32.7 5.1 6.8

44.4 94.3 37.8 38.8 36.2 23.6 17.9

All data18.3 64.3 20.7 39.7 8.9 14.4 1.1

34.3 69.9 31.0 39.7 30.6 25.3 18.0

Note: For each data source, first line is arithmetic average deviation, second line is mean absolute deviation.


8/15

8 SE-14-001

In SI units,C1= 235,C2= 206,uis in m/s,pin Pa,ifgin J/kg.

In I-P unitsC1= 70.3,C2= 0.314,uis in fpm,pin in. of Hg,

ifgin Btu/lb.

The wind velocity was measured at 0.3 m (3 ft) above the

water surface and the maximum was 1.3 m/s (264 fpm). There

must have been strong natural convection effects as water

temperature was always higher than the air temperature. Jones

et al.(1994) report that during the companion unoccupied pool

tests in this research program, water temperature was 29C and

the air temperature varied from 14.4C to 27.8C (58F to82F), with relative humidity from 27% to 65% . Thus, the

predictions of this formula at lower velocities do not represent

forced-convection effects. Their measurements at 200 fpm (1

m/s) and higher velocity are likely to be free of natural convec-

tion effects. Further, considering that Equation 2 is valid up to

a velocity of 0.15 m/s (30 fpm), the following equation is

proposed for forced-convection effects.

(7)

In SI units, a = 0.00005, b = 0.15 m/s. In I-P units, a = 0.0346,

b= 30 fpm.

This equation is plotted in Figure 3 along with the Smith

et al. correlation Equation 6. Also plotted in this figure is the

following formula given by Meyer (1942) which is among the

most verified for large reservoirs.

(8)

In SI units,a = 0.000116,b = 0.000126, andu in m/s. In I-P

units a = 0.0807, b = 0.000407,andu in fpm.

It is seen that the proposed formulas agrees closely with

with Equation 2 at the velocity of 0.15 m/s (30 fpm) and with

the formulasof Meyerand Smith et al.(1999) at higher veloc-

ities.As theSmith et al. (1999)measurements were only upto

a velocity of 1.3 m/s (254 fpm), agreement with the Meyer

formula at higher velocities gives confidence that Equation 7

can be used for a wide range of wind velocities.

Table 9. Air Density Difference at Typical Swimming Pool Conditions in SI Units

Water

Temp.,

C

Density Difference , kg/m3 Space Air Temperature and Relative Humidity

25C 26C 27C 28C 29C 30C

50% 60% 50% 60% 50% 60% 50% 60% 50% 60% 50% 60%

25 0.0185 0.0148 0.0135 0.0096 0.0084 0.0043 0.0034 0 0 0 0 0

26 0.0246 0.0209 0.0196 0.0157 0.0145 0.0104 0.0095 0.0051 0.0044 0 0 0

27 0.0308 0.0271 0.0258 0.0218 0.0207 0.0166 0.0156 0.0113 0.0105 0.0059 0.0054 0.0005

28 0.0370 0.0333 0.0320 0.0281 0.0270 0.0228 0.0219 0.0175 0.0168 0.0122 0.0116 0.0068

29 0.0434 0.0397 0.0384 0.0344 0.0333 0.0292 0.0282 0.0238 0.0231 0.0185 0.0180 0.0131

30 0.0498 0.0461 0.0448 0.0409 0.0397 0.0356 0.0347 0.0303 0.0295 0.0249 0.0244 0.0195

r w

r w

Table 10. Air Density Difference atTypical Pool Conditions in I-P Units

Water

Temp.,

F

Density Difference , lb/ft3 Space Air Temperature and Relative Humidity

76F 78F 80F 82F 84F 86F

50% 60% 50% 60% 50% 60% 50% 60% 50% 60% 50% 60%

76 0.0011 0.0009 0.0008 0.0005 0.0004 0.0002 0.0001 0 0 0 0 0

78 0.0015 0.0013 0.0012 0.0010 0.0008 0.0006 0.0005 0.0002 0.0001 0 0 0

80 0.0020 0.0017 0.0016 0.0014 0.0013 0.0010 0.0009 0.0006 0.0006 0.0003 0.0002 0

82 0.0024 0.0022 0.0020 0.0018 0.0017 0.0014 0.0013 0.0011 0.0010 0.0007 0.0006 0.0003

84 0.0028 0.0026 0.0025 0.0022 0.0021 0.0019 0.0018 0.0015 0.0014 0.0011 0.0011 0.0008

86 0.0033 0.0031 0.0029 0.0027 0.0026 0.0023 0.0022 0.0020 0.0019 0.0016 0.0015 0.0012

r w

r w

E0 a u/b 0.7

pw pa =

E a bu+ pw pa =


9/15

SE-14-001 9

Effect of Occupancy

Smith et al. (1999) report results of their tests on both

indoor and outdoor swimming pools, occupied and unoccu-

pied. They found no difference in the effect of occupancy on

evaporation rate between indoor and outdoor pools. This is

what would be expected from the physical phenomena

involved. Hence, Equation 5 is also applicable to outdoor

pools.

Effect of Solar Radiation and Radiation to Sky

Solar radiation adds heat to pool water and thus reducesthe energy needed for heating the pool. Further, the pool loses

heat by radiation to the sky, which has to be made up by addi-

tional heating.These heatgains andlosses have to be taken into

consideration in the calculation of pool energy requirements.

As seen in the formulas above, the rate of evaporation depends

only on the water temperature and air conditions. In heated

pools, water temperature is maintained constant by the heating

system, and, hence, loss or gain by radiation is not involved in

the calculation of evaporation. For unheated pools, water

temperature has to be calculated taking into consideration all

heat gains and losses, including those by radiation. The calcu-

lation of evaporation is then done using the calculated water

temperature.


for Outdoor Pools

The following calculation procedure is recommended for

outdoor swimming pools:

For unoccupied pools, calculate evaporation by Equa-

tions 1, 2, and 7. Use the largest of the three.

For occupied pools, calculate E0 as above and thenapply Equation 5.

POOLS CONTAINING HOT WATER

A notable example of pools with hot water is the pool for

storing spent fuel in nuclear power plants. During normal

operation, water temperature could be up to 50C (122F). If

cooling for the pool is lost during an abnormal/accidental

event, temperatures can rise to boiling point. The Shah

formula for natural convection has been verified for water

temperatures up to 94C (201F) Shah (2002). Figure 4 shows

Table 11. Comparison of Some Data Points for

Occupied and Unoccupied Swimming Pools with Various Formulas

Source

Pool

Area

m

2

(ft

2

)

Air

Temp.

C (F)

Air

RH,

%

Water

Temp.

C (F)

Numberof

Persons

Measured

Evapo-

ration

kg/m

2

h(lb/ft2h)

Percent Deviation From Formula of

ASHRAE

(2011)

VDI

(1994)

Smith

et al.

(1993,1999)

Hens

(2009)

Shah

(2013)

Biasin and

Krumme

(1974)

62.2

(669)

32.2

(90) 51.6

27.9

(82.2) 6

0.152

(0.031) 21.0 68.1 28.5 39.0 0.3

28.0

(82.4) 57.6

30.0

(86.0) 1

0.172

(0.035) 73.2 140.5 43.3 43.3 14.9

31.0 54.0 28.5 0 0.07 50.9 6.9 122.0 14.0 6.0

Heimann

and Rink

(1970)

200

(2149)

31.0

(87.8) 55.0

28.5

(83.3) 20

0.175

(0.035) 17.0 62.5 27.3 38.7 7.3

31.0

(87.8) 55.0

28.5

(83.3) 65

0.235

(0.048) 12.9 21.0 57.2 7.3 5.1

Doering(1979)

425(4568)

27.5(81.5)

34 25

(77.0) 35

0.212(0.043)

30.5 81.3 34.6 37.2 12.9

Hansen

and

Mathieson

(1990)

72

(774)

30.0

(86.0) 63

32

(89.6) 27

0.60

(0.122) 50.0 30.5 1.8 40.8 9.7

Hyldgaard

(1990)

418

(4493)

28.5

(83.3) 37.0

26.1

(79.0) 0

0.125

(0.026) 12.0 20.7 64.7 36.4 5.0

Bohlen

(1972) 32 (344)

27.0

(80.6) 60.0

25.0

(77.0) 0

0.052

(0.011) 42.3 0.9 110.8 19.1 1.0

Reeker

(1978)

Not

Given

25.5

(77.9) 71.0

23.0

(73.4) 0

0.026

(0.0054) 33.9 -5.1 95.7 23.0 7.0


10/15

10 SE-14-001

the comparison of the data of Boelter et al. (1946) with the

Shah formula. Air temperature during these tests varied from

19C to 25C (66.2F to 77.0F) and the relative humidity

from 64% to 98 %. The agreement is excellent throughout the

range of water temperature.

Hugo (2013) provided the author with preliminary datafrom the fuel pool of a nuclear power plant (Columbia Gener-

ating Station). The pool dimensions were 10.4 22.6 m (34

40 ft). He measured the increase in evaporation as water

temperature rose above 36.7C (98F). Air temperature was

25.5C (78F)and itsrelative humidity was57 %.Air velocity

above the pool was 0.31 m/s (62 fpm). To get the total evap-

oration, evaporation at 36.7C (98F) was calculated by the

Shah method described in the foregoing (largest of the values)

and added to the measurements at other water temperatures.

These were then compared with the Shah correlation as the

larger of the free and forced convection evaporation, as calcu-

lated with Equation 1 and 7. The comparison of measured and

predicted evaporation is shown in Figure 5. Good agreementis seen. Considering the good agreement with high tempera-

ture data of Boelter et al. (1946) and Hugo (2013), the Shah

method can be confidently used for high-temperature pools.

For ease in hand calculations, Tables 12 and 13 have been

prepared in SI and I-P units respectively. These list evapora-

tion rates at discrete values of temperature and relative humid-

ity, calculated as the larger of those from Equations 1 and 2.

Calculations for intermediate values can be done by linear

interpolation. Do not use these tables if air velocity is higher

than 0.15 m/s (30 fpm).


The following procedure is recommended for calculation

of evaporation from pools containing hot water:

Calculation procedure is the same as for unoccupied

swimming pools: calculate evaporation by Equations 1,

2, and 7 and use the largest of the three.

Calculations may alternatively be done with Table 12 or

13 if air velocity does not exceed 0.15 m/s (30 fpm).

Figure 3 Comparison of the proposed new formula for

evaporation, Equation 7, due to forced airflow,

with the formulas of Smith et al. (1999) and Meyer

(1944), 1 kg/m2h = 0.205 lb/ft2h, 1 m/s = 0.3048

ft/s.

Figure 4 Comparison of the data of Boelter et al. (1946)

with the predictions of the Shah correlation

(2012a), Equations 1 and 2, 1 kg/m2h = 0.205 lb/

ft

2

h.

Figure 5 Comparison of data of Hugo (2013) for evapora-

tion from a nuclear fuel pool with the Shah

formula. Building air temperature 25.5C (78F),

relative humidity 57%, 1 kg/m2h = 0.205 lb/ft2h.


11/15

SE-14-001 11

Table 12. Calculated Evaporation Rates at High Water Temperatures

by the Shah Correlation (2012a), Larger of Equations 1 and 2, SI Units

Water

Temp., oC

Air Temperature, C, and Relative Humidity, %

30C 35C 40C 45C 50C

30C 70C 30C 70C 30C 70C 30C 70C 30C 70C

35 0.443 0.246 0.350 0.116 0.236 0.023 0.138 0 0.096 0

40 0.707 0.485 0.608 0.332 0.495 0.165 0.033 0.033 0.184 0

45 1.057 0.816 0.951 0.644 0.830 0.448 0.691 0.232 0.530 0.047

50 1.516 1.26 1.403 1.072 1.274 0.853 1.126 0.603 0.956 0.325

55 2.113 1.845 1.992 1.643 1.855 1.405 1.698 1.128 1.517 0.809

60 2.879 2.603 2.752 2.390 2.607 2.137 2.441 1.839 2.251 1.489

65 3.856 3.576 3.721 3.352 3.569 3.088 3.396 2.775 3.198 2.403

70 5.088 4.809 4.948 4.578 4.790 4.306 4.661 3.983 4.407 3.598

75 6.632 6.358 6.486 6.123 6.323 5.847 6.140 5.520 5.932 5.130

80 8.550 8.288 8.400 8.053 8.234 7.778 8.049 7.453 7.840 7.066

85 10.92 10.67 10.76 10.44 10.60 10.17 10.41 9.859 10.21 9.487

90 13.81 13.60 13.66 13.38 13.49 13.12 13.31 12.83 13.12 12.48

Table 13. Calculated Evaporation Rates at High Water Temperatures

by the Shah Correlation (2012a), Larger of Equations 1 and 2, I-P Units

Water

Temp., F

Air Temperature, F, and Relative Humidity, %

90F 100F 110F 120F

30F 70F 30F 70F 30F 70F 30F 70F

100 0.111 0.063 0.087 0.029 0.058 0.004 0.031 0

110 0.182 0.128 0.157 0.088 0.27 0.043 0.092 0.006

120 0.278 0.220 0.251 0.175 0.22 0.122 0.183 0.062

130 0.408 0.346 0.379 0.297 0.345 0.238 0.306 0.168

140 0.58 0.516 0.549 0.463 0.513 0.399 0.471 0.323

150 0.805 0.740 0.772 0.684 0.735 0.617 0.691 0.536

160 1.097 1.032 1.063 0.975 1.023 0.905 0.978 0.821

170 1.471 1.408 1.435 1.35 1.395 1.28 1.349 1.195

180 1.946 1.887 1.91 1.829 1.869 1.760 1.823 1.677

190 2.544 2.491 2.507 2.435 2.467 2.37 2.423 2.291

200 3.290 3.246 3.254 3.194 3.215 3.134 3.173 3.064


12/15

12 SE-14-001

VARIOUS POOLS AND TANKS

For pools in residences, condominiums, hotels, and ther-

apeutic pools, the methods for indoor and outdoor swimming

pools presented earlier in this paper are recommended. The

ASHRAE HandbookHVAC Applications (2007, 2011)

recommends activity factors which give lower evaporation

rates from such pools compared to public pools. TheASHRAE activity factors are based on experience and prob-

ably indicate that these pools have loweroccupancy compared

to public pools. While calculating evaporationwiththe present

method, occupancy based on experience should be used.

Water pools are often provided inside and outside build-

ings to enhance aesthetics. In hot, dry climates, water pools

provide evaporative cooling in naturally ventilated buildings.

Outdoor pools are often used to provide cooling water for the

condensers of refrigeration plants. Evaporation in all such

pools can be calculated by the methods presented earlier for

unoccupied indoor and outdoor swimming pools.

The same methods are recommended for various tanksand vessels containing water.

EFFECT OF EDGE HEIGHT OR LOW WATER LEVEL

If the water level is lower than the top edge of the pool or

vessel, one will expect some impairment of natural convection

currents and hence some reduction in evaporation. This effect

will be expected to increase with increasing (/d) where isthe edge height andis the equivalent diameter of the vesselor pool. This possible effect has been investigated by several

researchers.

Sharpley and Boelter (1938) measured evaporation into

quiet air from a 0.305 m (1 ft) diameter pan. The water level

was flush with top. Tests were also performed with water level

12.7 and 38.1 mm (0.5 and 1.5 in.) below the top edge. Thus,

(/d) varied from 0 to 0.125. Sharpley and Boelter found noeffect of liquid level variation. Hickox (1944) also did similar

tests. His data do not show any clear effect of level variation.

Stefan (1884) measured evaporation from tubes of diam-

eter 0.64 to 6.16 mm (0.025 to 0.24 in.) and depth below the

rim of 0 to 44 mm (0 to 1.7 in.). He found the evaporation rate

to be inversely proportional to the depth. Considering the

larger tube, (/d) at 44 mm (17.3 in.) depth below the topwould be 7.1. As noted earlier, reduction in evaporation at

large (/d) is expected as inward and outwards movement of

natural convection streams of air will be hampered. At verylarge depths, evaporation will be entirely due to molecular

diffusion.

For large values of (/d), evaporation by forced convec-tion will also be impaired as airstream will be unable to

remove the air layers near the water surface.

In swimming pools, the water level is close to the top and

hence there is no reduction in evaporation. For other types of

pools and vessels in which water level is very low, the predic-

tions by the Shah method will need to be corrected. Details of

Stefans tests are not available and no other test data were

found.Basedon theresults of Stefan(1884) mentionedearlier,

the following is tentatively suggested as a rough guide:

(9)

WhereEshahis the evaporation rate by the Shah method and

Emd is the evaporation by molecular diffusion. Methods tocalculate evaporation by molecular diffusion are explained in

text books as well as in Chapter 6 of the ASHRAE Hand-

bookFundamentals(2013).

EVAPORATION FROM WATER SPILLS

Water spilled on the floor will cool down fairly quickly,

approaching the wet-bulb temperature of air. If it reaches the

wet bulb temperature, the difference of density between room

air and the air at water surface will be zero, there will be no

natural convection, and evaporation will be due to forced

convection. Hence, the following simple method is suggested

for approximately calculating evaporation rate from spills:

1. Assume water temperature to be equal to the wet-bulb

temperature of air.

2. For spills inside buildings, use Equation 2 to calculate

evaporation.

3. For outdoor spills, use Equation 7 to calculate evapora-

tion.

More rigorous transient calculations may be done with a

computer model that takes into consideration heat transfer

between the floor and water together with heat and mass trans-

fer between air and water. The Shah correlation may be incor-porated into such a model.

SUMMARY OF

RECOMMENDED CALCULATION METHODS

The calculation methods recommended in the foregoing

are summarized in Table 14.

CONCLUSION

In this paper, methods for calculating evaporation from

many types of pools and other water surfaces were presented

and discussed. These include the authors published correla-tions for indoor occupied and unoccupied swimming pools.

Also presented were methods for outdoor occupied and unoc-

cupied swimming pools, hot-water pools such as nuclear fuel

pools, decorative pools, tanks and vessels/containers, and

water spills. These methods are based on theory, physical

phenomena, and test data. A number of look-up tables were

provided for easy manual calculations.

More tests to collect data on evaporation from swimming

pools is highly desirable, especially for occupied pools as data

from only four sources could be found.

For /d 1 , E Eshah /d is Emd=


13/15

SE-14-001 13

ACKNOWLEDGEMENT

The author thanks Mr. Bruce Hugo for providing the data

from hisongoing tests on evaporationfrom a nuclear fuel pool.

Thanks are also due to Mr. Rui Igreja for checking the look-

up tablesin theauthors previous publicationsand pointing out

some discrepancies.

NOMENCLATURE

A = area of water surface, m2 (ft2)

d = diameter or equivalent diameter of vessel/tank, m

(ft). Equivalent diameter = (A/0.785)0.5

D = coefficient of molecular diffusivity, m2/h (ft2/h)E = rateof evaporation under actual conditions, kg/m2h

(lb/ft2h)

Eocc = rate of evaporation from occupied swimming pool,

kg/m2h (lb/ft2h)

E0 = rate of evaporationfrom unoccupied pools,kg/m2h

(lb/ft2h)

FU = pool utilization factor, = 4.5N* (42N*), dimension-

less

g = acceleration due to gravity, m/s2 (ft/s2)

Gr = Grashof number, dimensionless

ifg

= latent heat of vaporization of water, J/kg (Btu/lb)

hM = mass transfer coefficient, m/h (ft/h)

L = characteristic length m (ft)

N = number of pool occupants

N* = N/A, persons/m2 (persons/ft2)

Nu = Nusselt number, dimensionless

p = partial pressure of water vapor in air, Pa (in. Hg)

Pr = Prandtl number, dimensionless

ReL = Reynolds number = uL/, dimensionlessSc = Schmidt number =/D, dimensionless

Sh = Sherwood number, =hML/D, dimensionless

u = air velocity, m/s (fpm)

W = specific humidity of air, kg of moisture/kg of air (lb

of moisture/lb of air)

x = concentationof moisture inair,kg ofwater/m3 of air

(lb of moisture/ft3 of air)

x = (xwxr), kg/m3 (lb/ft3)

Greek Symbols

= depth of water level below top edge, m (ft)

= dynamic viscosity of air, kg/mh (lb/fth) = density of air, mass of dry air per unit volume ofmoist air, kg/m3 (lb/ft3) (This is the density in

psychrometric charts and tables)

= (rw), kg/m3 (lb/ft3)

Subscripts

a = of air away from the water surface

H = heat transfer

M = mass transfer

r = at room temperature and humidity

w = saturated at water surface temperature

APPENDIX

Derivation of Formula for Evaporation by

Natural Convection

The formula is derived using the analogy between heat

and mass transfer, considering the water surface to be a hori-

zontal plate with the heated face upwards.

The rate of evaporation is given by the relation (Eckert

and Drake 1972)

Table 14. Summary of Recommended Calculation Methods

Application Calculation Method Notes

Indoor swimming pool, unoccupied Use larger of Equations 1 and 2 Tables 4 and 5 may be used for manual calculations

Indoor swimming pool, occupied Use Equation 5 Tables 9 and 10 may be used with Tables 4 and 5 for

manual calculations

Outdoor swimming pool, unoccupied Use largest of Equations 1, 2, and 7

Outdoor swimming pool, occupied Use Equation 5 E0by the method for outdoor unoccupied pools

Various types of pools, indoor or outdoor Same as for unoccupied swimming pools For indoor hot-water pools, Tables 12 and 13 may

be used for manual calculations

Vessels, tanks, containers Same as for unoccupied swimming pools If water level is very low, correct prediction with

Equation 9

Water spills

Assume water is at wet-bulb temperature

of air and then calculate as for unoccupied

swimming pool

For more accuracy, perform computerized transient

calculations considering all factors


14/15

14 SE-14-001

(A1)

The air densityhas been evaluated at the water surfacetemperature as recommended by Kusuda (1965).

Heat transfer during turbulent natural convection to a

heated plate facing upwards is given by the following relation

(McAdams 1954):

(A2)

Using the analogy between heat and mass transfer, the

corresponding mass transfer relation is

(A3)

GrMis defined as (Eckert and Drake 1972)

(A4)

where

(A5)

Equation A5 may be approximately written as

(A6)

Combining Equations A4 and A6

(A7)

Using Equation A7 and the definitions of Sh and Sc,

Equation A3 becomes

(A8)

Combining Equations A1 and A8:

(A9)

The value of (D2/3 1/3) doesnot vary much overthe typi-calrangeof room airconditions.Inserting a mean value, Equa-

tion A9 becomes:

(A10)

withC= 35 in SI units and 290 in I-P units.

It is noteworthy that Equations A9 and A10 have been

derived from theory without any empiricaladjustments. Equa-

tion A10 was first published in Shah (1992); the detailed deri-

vation was published in Shah (2008).

Derivation of Formulas for Evaporation by

Forced Convection

For heat transfer during flow of air over a heated horizon-

tal plate with turbulent flow, the mean Nusselt number for theplate is given by

(A11)

Using the analogy between heat and mass transfer, the

corresponding mass transfer relation is

(A12)

The viscosity and Schmidt number of air change very

little over the typical air conditions. Taking a mean value for

them and substituting an empirical relation for the coefficient

of diffusivity, the following formula is obtained for air-waterin SI units.

(A13)

Where u is the free stream velocity in m/min andL is the

length of pool in the direction of air in meters.

In I-P units, the equation is:

(A14)

Whereuis in fpm andLis in feet..

The above derivation is from Shah (1981).

REFERENCES

ASHRAE. 2007. ASHRAE HandbookHVAC Applications.

Atlanta: ASHRAE.

ASHRAE. 2011. ASHRAE HandbookHVAC Applications.

Atlanta: ASHRAE.

ASHRAE 2013. ASHRAE HandbookFundamentals.

Atlanta: ASHRAE.

Biasin, K., and W. Krumme. 1974. Die wasserverdunstungin einem innenschwimmbad. Electrowaerme Interna-

tional32(A3):A115A129.

Boelter, L.M.K., H.S. Gordon, and J.R. Griffin. 1946. Free

evaporation into air of water from a free horizontal quiet

surface. Industrial & Engineering Chemistry38(6):596

600.

Bohlen, W.V. 1972. Waermewirtschaft in privaten, geschlos-

senen SchwimmbaedernUberlegungen zur Auslegung

und Betriebserfahrungen, Electrowaerme International

30(A3):A139A142.

E0 hMw Ww Wr =

Nu 0.14 GrHPr 1/3

=

Sh 0.14 Gr MSc 1/3

=

GrMg Ww Wr L

3

2

2

-----------------------------------------------=

1---

W---------

=

r w

Ww Wr -------------------------------=

GrMg

r

w

L3

2-------------------------------------

=

hML

D----------- 0.14

r w g L3

D---------------------------------

1/3

=

E0 0.14g1/3

D2/3

1/3

w r w 1/3

Ww Wr =

E0 Cw r w 1/3

Ww Wr =

Nu 0.036 ReL 836 Pr1/3

=

Sh 0.036 ReL 836 Sc1/3

=

E0 0.0016t 0.22+ L 1

=

2.54 Lu a 0.8

256 w Ww Wa

E0 0.0092t 2.07+ L 1

=

3.5 Lu a 0.8 256 w Ww Wa


15/15

SE 14 001 15

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